# Using Constant or float for scalar constant

**URL:** <https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971>\
**Category:** General\
**Created:** [June 13, 2024, 11:51am UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971 "2024-06-13T11:51:21Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![RR\_rr](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rr_rr/32/6571_2.png) [@RR\_rr](https://fenicsproject.discourse.group/u/RR_rr)\
**Post date:** [June 13, 2024, 11:51am UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/1 "2024-06-13T11:51:21Z")

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Dear all,  
In fenics, we can use Constant for a scalar constant, for example `f=Constant(-6.0)`, and alternatively we can use float for a scalar constant, for example `f=-6.0`. I wonder what’s the difference between these two usages? Below is the Poisson problem code from fenics tutorial. I changed the `f = Constant(-6.0) ` to `f = -6.0`, and the result didn’t change. So what’s the meaning of using Constant for a scalar constant? We can just simply use float type for a scalar constant, like this: `f = -6.0`.  
My second question is are the `Constant((0, 1))` and `as_vector([0, 1])` the same?

I appreciate any help. Thank you very much in advance.

```auto
from __future__ import print_function
from fenics import *
import matplotlib.pyplot as plt

# Create mesh and define function space
mesh = UnitSquareMesh(8, 8)
V = FunctionSpace(mesh, 'P', 1)

# Define boundary condition
u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2)

def boundary(x, on_boundary):
    return on_boundary

bc = DirichletBC(V, u_D, boundary)

# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)

#test Constant and float
# f = Constant(-6.0)
f = -6.0

a = dot(grad(u), grad(v))*dx
L = f*v*dx

# Compute solution
u = Function(V)
solve(a == L, u, bc)

# Plot solution and mesh
plot(u)
plot(mesh)

# Save solution to file in VTK format
vtkfile = File('poisson/solution.pvd')
vtkfile << u

# Compute error in L2 norm
error_L2 = errornorm(u_D, u, 'L2')

# Compute maximum error at vertices
vertex_values_u_D = u_D.compute_vertex_values(mesh)
vertex_values_u = u.compute_vertex_values(mesh)
import numpy as np
error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))

# Print errors
print('error_L2 =', error_L2)
print('error_max =', error_max)

# Hold plot
plt.show()

```

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**Author:** ![francesco-ballarin](https://avatars.discourse-cdn.com/v4/letter/f/f05b48/32.png) [@francesco-ballarin](https://fenicsproject.discourse.group/u/francesco-ballarin)\
**Post date:** [June 13, 2024, 4:07pm UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/2 "2024-06-13T16:07:49Z")

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> [@RR\_rr](#):
>
> We can just simply use float type for a scalar constant, like this: `f = -6.0`.

You could, but if one day you decide that your `f` must change to `-6.1`, the form compiler will recompile the form from scratch. By using `Constant` you are informing the form compiler that the value of `f` is a constant (regardless of its actual value), and you’ll be allowed to change it in future without triggering a recompilation.

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**Author:** ![RR\_rr](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rr_rr/32/6571_2.png) [@RR\_rr](https://fenicsproject.discourse.group/u/RR_rr)\
**Post date:** [June 14, 2024, 9:54am UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/3 "2024-06-14T09:54:10Z")

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I understand now. Thank you for your reply. Besides, I wonder if `Constant((0, 1))` and `as_vector([0, 1])` the same. 🙂

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<div class="post-metadata">

**Author:** ![francesco-ballarin](https://avatars.discourse-cdn.com/v4/letter/f/f05b48/32.png) [@francesco-ballarin](https://fenicsproject.discourse.group/u/francesco-ballarin)\
**Post date:** [June 14, 2024, 11:39am UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/4 "2024-06-14T11:39:55Z")

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They are not

```auto
>>> import ufl
>>> ufl.as_vector([0, 1])
ListTensor(Zero((), (), ()), IntValue(1))

```

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<div class="post-metadata">

**Author:** ![RR\_rr](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/rr_rr/32/6571_2.png) [@RR\_rr](https://fenicsproject.discourse.group/u/RR_rr)\
**Post date:** [June 15, 2024, 10:16am UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/5 "2024-06-15T10:16:48Z")

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Got it. Thank you. But if we want to define a constant vector (0, 1) in fenics, which one is better?

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<div class="post-metadata">

**Author:** ![francesco-ballarin](https://avatars.discourse-cdn.com/v4/letter/f/f05b48/32.png) [@francesco-ballarin](https://fenicsproject.discourse.group/u/francesco-ballarin)\
**Post date:** [June 15, 2024, 4:33pm UTC](https://fenicsproject.discourse.group/t/using-constant-or-float-for-scalar-constant/14971/6 "2024-06-15T16:33:59Z")

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I’d say `Constant`, especially if you plan to change those entries in the future.